《保险研究》20200709-《基于非齐次Markov模型的长期护理保险定价研究》（张琳、汤薇）

［摘   要］本文运用四状态时间非齐次马尔科夫模型对65~105岁老年人的健康转移强度建模,在Tweedie-GLM模型的框架下,加入年龄效应、时间趋势和年龄-时间交互效应。实证结果表明,除了常见的年龄效应外,时间趋势和年龄-时间交互作用也是解释健康状态转移的重要因素。本文还基于精算理论预测预期寿命和护理需求期望时间,并给出2020年的长期护理保险精算费率表,结果发现在各个时刻下的女性,相较于相同年龄和初始健康状态下的男性都具有绝对的生存优势；虽然在2002~2012年男性具有健康优势,但随着时间的推移,男性在失能状态的持续时间将超过女性,而女性在受损状态的持续时间一直稳步超过男性,二者叠加使得2020年初始状态为失能的男性长期护理保险费率显著高于女性。

［关键词］非齐次Markov；健康转移概率；失能；长期护理保险

［作者简介］张琳,湖南大学风险管理与保险精算研究所所长、金融与统计学院教授,E-mail:lindazhang0203@126.com；汤薇,上海财经大学金融学院博士。

Long Term Care Insurance Pricing Based on the Non-homogeneous Markov Model

ZHANG Lin,TANG Wei

Abstract：This paper used the four-state time non-homogeneous Markov process to model the health transfer intensity of elderly people aged from 65 to 105 under the framework of Tweedie-GLM model,and also added factors such as age effects,time trends,and age-time interactions.The empirical results show that in addition to the common age effects,time trends and age-time interactions are also important factors in explaining the shift of health status.This paper also predicted life expectancy and expected time length of nursing needs based on actuarial theories,and created a long-term care insurance actuarial rating table for 2020.The results show that at all times and under the same age and initial health status conditions,females have an absolute survival advantage over males.Although males have a health advantage between 2002 and 2012,their disability time duration will last longer than females over time.But women′s time duration of impairment has steadily surpassed that of men.As a combined result of these two situations,the premium rate of long-term care insurance for initially disabled males in 2020 is significantly higher than females.

Key words：non-homogeneous Markov;health transfer probability;disability;long-term care insurance